Final answer:
True, the difference between the actual y-value and the predicted y-value in a regression equation is indeed called the residual, which measures the discrepancy between observed data and the model's estimation.
Step-by-step explanation:
The statement that the difference between the actual y-value and the predicted y-value found using a regression equation is called the residual is true. In regression analysis, the predicted y-value, often denoted as ŷ (read as 'y hat'), is the value estimated from the regression line. The actual y-value is the observed data point. When subtracting the predicted y-value from the actual y-value (y - ŷ), one obtains the residual for that data point. This residual reflects the discrepancy between the observed data and the regression model's estimation.
If the observed data point lies above the regression line, the residual is positive, indicating that the line underestimates the actual data value for y. Conversely, if the data point lies below the regression line, the residual is negative, showing that the line overestimates the actual y-value. Residuals are crucial in regression analysis as they help identify the goodness of fit for the regression model and can be used to detect outliers or patterns that may violate the analysis assumptions.